I'd request accountancy services if you take the job, then you'll be in good hands. The laws are tricky and can depend upon the number of days that you are in and out of the UK. The tax rates in the 2 countries are essentially the same (if you look at UK tax and NI tax compared to US fed, state, local, etc). However, the UK no longer offers mortgage interest and property tax deductions and other things the IRS offers. Therefore, our taxes are much higher in the UK than they were in the US. You'll want to check this carefully (I posted the rates for both countries elsewhere on this site or you can do a search for them).
You are correct in that the first 80K is excluded IF you meet the requirements (physical presence test). You'll want to watch this if you transfer mid-year/end of year.
The inland rev system works on an April-March fiscal year, not a Jan-Dec schedule.
You'll also want to check into the pension schemes: some or many cannot be touched until age 65, so if you only plan to be over for a few years then the penalties may not be worth it. You'd want some IRAs or such instead--again up to your advisors and your preference.
We are preparing now to leave the UK and return to the US and we can file to receive some tax back, but that is our personal allowance tax, etc. that we get back for leaving mid-tax year. In the UK we do not file returns--tax rates are standard and your employer will manage this (it also means there isn't as much room for deductions).
Personally I feel that London rents are on par with NY and SanFra--my friend in SF pays the same we do but her place is twice the size of ours. I've no idea how Washington compares. It all depends where you want to be.
90k would be a good wage, but as the others say it all depends on your industry. Some positions come with a car allowance and some do not (there can be tax implications). The avg UK wage is 25K or so. Think of most things as costing in pounds what they cost in dollars: a coffee is 3 pounds instead of 3 dollars, etc. 90K is doable, but there's no easy way to say how it compares to your lifestyle now. Going out to dinner is much more expensive as are clothes (I think but some groceries are less). Cars are much more expensive (so is car tax, petrol) but if you are in London then you'll take public transport or walk to work, in all probability (parking is a nightmare--it's always pay and always a challenge).
Look at
www.findaproperty.com to get some London rent prices.
Whatever you do, approach this as a 1 or 2 year transfer and not a forever thing...it's easier to grasp the tax info and such one step at a time.
Good luck!